**OVERVIEW
**
In the last 10-15 years the theory of linear algebraic groups has witnessed
an intrusion of the cohomological methods of modern algebraic geometry and
algebraic topology. These new methods have led to breakthroughs on a number
of classical problems in algebra, which are beyond the reach of earlier purely
algebraic techniques. The workshop will focus at the following new emerging
techniques and applications:

- The proof of the Grothendieck-Serre conjecture based on the theory of affine
Grassmannians.

The Grothendieck-Serre conjecture stated in 60's says that any rationally
trivial G-bundle is locally trivial (in Zariski topology), where G is a smooth
reductive group scheme over a local regular ring. In a recent preprint (Nov.
2012) Fedorov and Panin proved the conjecture in the geometric case using
new connections with the theory of affine Grassmannians.

- Computation of generalized equivariant cohomology of projective homogeneous
and toric varieties.

The notion of an algebraic oriented cohomology theory was introduced and extensively
studied during the last decade by Levine, Morel, Panin, Smirnov and others.
The universal such theory called algebraic cobordism has many applications
in the theory of quadratic forms and homogeneous spaces. Its equivariant version
is believed to contain all the information concerning cohomological behaviour
of homogeneous spaces. In particular, its computation can lead to a better
understanding of cohomology and related combinatorics of toric varieties.

**OUTLINE OF THE PROGRAM**

The workshop will run for three full days and a morning session during the
fourth day (Friday morning - Monday noon) and will feature a unique combination
of two introductory mini-courses and research-level talks. The two mini-courses
will have three 80 min. lectures each and directed towards PhD students and
young researchers. The topics are the following.

(a) Toric varieties and equivariant cohomology by Kalle Karu, University of
British Columbia

- The course will be an introduction to toric varieties and equivariant cohomology.

(b) Introduction to principal homogeneous spaces by Roman Fedorov, Kansas
State University

- The course will be devoted to the basics in the theory of torsors and the
Grothendieck-Serre conjecture.

Besides the two mini-courses, there will be invited one-hour talks by the
leading experts in the area, as well as short talks by young researchers,
postdocs and graduate students.

**INVITED SPEAKERS confirmed as of January 3, 2014**

Alex Duncan, University of Michigan

Stefan Gille, University of Alberta

Nikita Karpenko, University of Alberta

Daniel Krashen, University of Georgia

Nicole Lemire, Western University

Alexander Merkurjev, University of California at Los-Angeles

Julia Pevtsova, University of Washington

Andrei Rapinchuk, University of Virginia

Zinovy Reichstein, University of British Columbia

**FINANCIAL SUPPORT**

Some funding is available for graduate students and postdoctoral fellows.
Please, apply via the web-site of the workshop.

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Participants may also be interested in a closely related event, the 73rd
Algebra Day on April 27, 2014, also at the University of Ottawa.

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